Partial affine spaces of dimension ≥ 3

An incidence structure with parallelism is said to be a partial affine space if it is embeddable in an affine space with the same pointset preserving the parallelism. Hence partial affine spaces are isomorphic to affine spaces, in which only complete parallel classes of lines are allowed to be missing. The dimension of a partial affine space is defined to be equal to the dimension of the corresponding affine space. In this article, at least three-dimensional partial affine spaces will be characterized as partial linear spaces with parallelism fulfilling certain axioms. Dedicated to Professor H. Mäurer on the occasion of his 60th birthday